Non-equidistance Multivariate Fractional Order Accumulation NFMGM (1, n) Model Based on the Background Value Optimization

Author(s): 
Y. X. Luo & Q. Y. Liu

ABSTRACT: Based on the integral and index characteristics of the grey model GM (1, 1), the fractional order accumulation generation sequence can be fitted by means of inhomogeneous exponential. The present paper has proposed the method of structure non-equidistance multivariate fractional order accumulation NFMGM (1, n) model background values and provided the formula of structure background value. The non-equidistance multivariate fractional order accumulation gray NFMGM (1, n) model based on the background value optimization has been proposed in the present paper. In the process, the inhomogeneous exponential function is employed for fitting accumulation generation r order sequence, the original data sequence of the first component is used as the initial conditions of grey differential equation, the minimum relative error is as the objective function, the fractional order number, the initial value of the correction and background value parameters has been used as design variables. The model has the characteristics of high precision and using simply, which is not only suitable for equidistance model, also suitable for the non-equidistance. Examples show that the model of practicality and reliability.

Keywords : NFMGM (1, n) model; Background value; Fractional order accumulation generation Non-equidistance sequence; Optimizing.